There are thousands of fonts, there is no clear answer of what is best for ___ website or ___ page. It's all what you think looks good and sometimes depends on the colors on the site.
Answer is "Web Designer".
Web Designers are the "artists" of the website. They conceptualize the layout and functionality of the site, from features to format. They may do little coding, and are mostly involved in the creative elements of web design. The Web Developer is less big-picture, and more knitty-gritty building of the website. She is the one who does the coding and actually builds the website, using the web designer's model.
The answer to the given picture is - Microsoft word's spell checker only recognizes very common words. Microsoft word has it's own dictionary which will be compared to the texts on your document. If they see an unfamiliar word they will underline it with red. Anyways you can add your own words and names to the custom dictionary.
